Calculate Ksp from molar solubility (BaCrO₄, A₃B₂) and Q vs Ksp
The solubility product Ksp is the equilibrium constant for dissolving a sparingly soluble ionic solid. For a salt that dissolves as x cations and y anions per formula unit, Ksp = [cation]^x[anion]^y at saturation. Molar solubility s is the moles of formula unit that dissolve per liter of saturated solution in pure water.
To calculate Ksp from solubility, write the dissolution equation, express each ion as a multiple of s, and multiply. Example: AgCl (type AB) with s = 1.34×10⁻⁵ M gives Ksp = s² ≈ 1.8×10⁻¹⁰. BaCrO₄ is the same AB pattern: s = 1.08×10⁻⁵ M → Ksp = s² = 1.17×10⁻¹⁰. For A₃B₂ (e.g. a homework salt or Ca₃(PO₄)₂), Ksp = 108 s⁵. To find Ksp the other way, invert the same relation: s = √Ksp for AB, or s = (Ksp/4)^(1/3) for AB₂ / A₂B.
Comparing the ion product Q (same form as Ksp but with actual concentrations) to Ksp predicts precipitation: Q > Ksp favors solid formation, Q < Ksp means the solution is unsaturated. The Ksp Calculator converts between s and Ksp for common salt stoichiometries and evaluates Q versus Ksp as a precipitation reaction check.
- AB salt: Ksp = s²
- AB₂ salt: Ksp = 4s³
- A₂B salt: Ksp = 4s³
- A₃B₂ salt: Ksp = 108 s⁵
- Q > Ksp → precipitate expected
Formulas you will actually use
For MxAy(s) ⇌ x M + y A with solubility s:
Ksp = (x s)^x (y s)^y = x^x y^y s^(x+y)
s = (Ksp / (x^x y^y))^(1/(x+y))
Q = [M]^x [A]^yStep-by-step example: Solubility of AgCl from Ksp
AgCl is type AB with Ksp = 1.8×10⁻¹⁰ at 25 °C. Find the molar solubility in pure water.
- Ksp = s² = 1.8×10⁻¹⁰.
- s = √(1.8×10⁻¹⁰) ≈ 1.34×10⁻⁵ mol/L.
Choose Ksp → solubility, salt type AB, Ksp = 1.8e-10.
Step-by-step example: Ksp of BaCrO₄ from molar solubility
The molar solubility of BaCrO₄ in pure water is 1.08×10⁻⁵ M. Calculate Ksp.
- BaCrO₄ is type AB: BaCrO₄(s) ⇌ Ba²⁺ + CrO₄²⁻.
- Ksp = s² = (1.08×10⁻⁵)² = 1.166×10⁻¹⁰.
Choose Solubility → Ksp, type AB, s = 1.08e-5, or use the BaCrO₄ chip.
Step-by-step example: Hypothetical A₃B₂ salt
The solubility of A₃B₂ is 6.1×10⁻⁹ mol/L. A₃B₂(s) ⇌ 3A²⁺ + 2B³⁻. What is Ksp?
- [A] = 3s, [B] = 2s.
- Ksp = (3s)³(2s)² = 108 s⁵.
- s = 6.1×10⁻⁹ → Ksp ≈ 9.12×10⁻⁴⁰.
Choose Solubility → Ksp, salt type A₃B₂, s = 6.1e-9, or use the A₃B₂ chip.
Frequently asked questions
How do I calculate Ksp from molar solubility?
Write the ions produced per formula unit, replace each with a multiple of s, and multiply. AB salts: Ksp = s². AB₂ or A₂B: Ksp = 4s³. A₃B₂: Ksp = 108 s⁵. Enter s in the Ksp Calculator’s solubility → Ksp mode and pick the matching salt type.
How do I find Ksp from a homework solubility string?
Identify the salt type, then use solubility → Ksp. BaCrO₄ is AB: Ksp = s². For a hypothetical A₃B₂ salt (3A + 2B), Ksp = 108 s⁵. Chips for BaCrO₄ (s = 1.08×10⁻⁵) and A₃B₂ (s = 6.1×10⁻⁹) load those problems. If you are given Ksp instead, invert: s = √Ksp for AB, s = (Ksp/4)^(1/3) for AB₂ / A₂B.
Is this a precipitation reaction calculator?
For the Q vs Ksp test, yes. Enter the actual ion concentrations to get Q. Q > Ksp predicts a precipitate; Q < Ksp means no solid yet; Q = Ksp is saturated. It does not write a full net-ionic precipitation equation—use the Chemical Equation Balancer for that.
What are the units of Ksp?
As a true thermodynamic equilibrium constant Ksp is unitless (activities). In classroom problems that use molarity, people quote (mol/L)^{x+y}: s² for AB, 4s³ for AB₂, 108 s⁵ for A₃B₂. Homework usually wants the number only. This calculator reports Ksp from concentrations in mol/L.
Can I find Ksp from pH?
Only if you already know how [H⁺] maps onto the dissolving ions (hydroxides, carbonates). That is a hydrolysis / ICE problem, not a one-step Ksp conversion. Use solubility → Ksp or Q vs Ksp here, and the Chemical Equilibrium Calculator for the ICE table.
Does this include the common-ion effect?
The s ↔ Ksp modes assume pure water (no extra common ion). For common-ion problems, set up the ICE table with the extra ion and use the Chemical Equilibrium Calculator or solve algebraically; you can still check Q vs Ksp with measured ion concentrations.
Are Ksp values temperature-dependent?
Yes. Tabulated Ksp values are for a stated temperature (often 25 °C). Using a Ksp at the wrong temperature gives the wrong solubility.
References & further reading
Standards bodies, university open courseware, and peer-reviewed references that align with the methods used on this page.
See also: Chemical Equilibrium Calculator · Chemical Equation Balancer · pH Calculator
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